Probability question?

Question

Harry and Malfoy alternately toss a die (Harry first, followed by Malfoy). The one who gets bigger number is the winner, the game will continue if both of the get the same number. Find the probability that

a) Harry will be the winner after the first toss of Malfoy
b) Harry is the winner

Answer 1

**None of the previous responses have so far been right.

Part (a): There are obviously six possibilities for every toss of the dice, and for each toss by Harry, there are six possible outcomes of the follow-up toss by Malfloy. This gives 36 possible outcomes. Each of these values imposes a certain chance for the probability of rolling a higher number. For instance, if 6 was rolled then there is obviously a 0/6 or 0% chance of rolling a higher number, whereas if 1 was rolled there is a 5/6 chance of rolling a higher number. Notice, also that for each possible value there is a 1/6 chance that the same number is rolled, and thus no winner determined. The probability of Harry winning is based on the chance for Malfloy to toss an equal or greater value. If you examine each set of two tosses, ie Harry tosses a 1, Malfloy tosses a 1 etc. You will come to the conclusion that 6 of the pairs end in a tie, 15 end with Harry as the winner and 15 end with Malfloy winning. So
a.) 15/36 = 42%

Part (b): Because we are not concerned with individual tosses, we do not have to worry about the possibility of a tie. In the case of a tie, the games just continues so it does not add to the overall probability of a winning. Notice that the numbers on a dice would have a median between three and four, this splits the set of numbers on the die into two groups, one having greater values than the other. The groups are equal size, each has three elements. The lower group is: 1,2,3. The higher group is: 4,5,6. Since the groups are equal in size, there is a fifty percent chance to roll a number belonging to the greater-valued group, therefor the answer is 50%.

b) 1/2 = 50%

Of course, Malfloy will use magic to cheat, so in reality Harry has a zero percent chance to win. Best of luck with others like this.

Answer 2

Unless I misunderstand the question going first does not offer an advantage. Harry's chance of winning on the first matchup is 5/12 and so is Malfoy's. There is a 2/12 = 1/6 chance the game will continue. Since neither side has an advantage, ultimately the chance of Harry winning is 1/2. More formally, you could sum the infinte series 5/12 + (5/12)(1/6) + (5/12)(1/6)^2+... = 1/2

Answer 3

Hope this explanantion is not too long but I want you to understand the answer:

There are 36 different combinations for Harry's and Malfoy's rolls where the first number represents Harry's roll and the second is for Malfoy:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
If Harry rolls a 1 he has no chance of winning. He can only hope for a tie if malfoy rolls a one as well. If Harry rolls a 2 then there is ONE chance for him to win if Malfoy rolls a one. And if Harry rolls a 6, then there are 5 chances for him to win as Malfoy can only tie with a 6. In any event, out of the 36 possible combinations listed, 15 of them end up in Harry winning. So the chances of Harry winning on the first try is 15/36. The chances of Malfoy winning on the first try is ALSO 15/36 and the chances of a tie are 6/36.

The chances of Harry eventually winning regarless of round is simply 1/2, or 50% as neither player has any advantge over the other and the chances of one person winning is the SAME as the other person.

The answer to the first question is not apparent to all people as they forget that a game may end in a tie. So even though the chances of them winning are the same its actually not simply 50%.

Once again
A. 15/36
B. 1/2 or simply, 50%

Answer 4

a.). 5/6
b.). 5/6

actually i just guessed the answer.
use a probability diagram to solve this question to get the right answer!
good luck!

Answer 5

part a

well the chances of winning are 50%
it doesnt seem like part a and part b are different.

Answer 6

Improbability question!